Thomas Q. Sibley
Professor Emertus of Mathematics
College of St. Benedict and St. John's University
St. Jospeh, MN 56374
e-mail: t.sibley@retiree.csbsju.edu
I retired in 2021.
My coming book, Exploring Discrete Geometry, has been accepted for publication by the MAA (Mathematical Association of America) in the Anneli Lax series. This series has for its target audience high school students excited about mathematics. I hope the "spiral" format of my book fits this group. The first chapter asks easily envisioned questions in six areas of discrete geometry, a topic I'm confident high school students have never encountered. The next chapter answers these questions, provides some context, and then twists each of them in various ways to ask deeper questions. Chapter Three continues this process of answering and twisting the questions. The final chapter answers this latest round and then describes the current state for these questions-sometimes with unsolved problems, sometimes with descriptions of deep results beyond high school level.
My abstract algebra text, Thinking Algebraically: An Introduction to Abstract Algebra was published by the MAA/AMS in 2022. The description below is from the back cover.
Thinking Algebraically
presents the insights of abstract algebra in a welcoming and accessible way.
It succeeds in combining the advantages of rings-first and groups-first
approaches while avoiding the disadvantages. After an historical overview,
the first chapter studies familiar examples and elementary properties of groups
and rings simultaneously to motivate the modern understanding of algebra. The
text builds intuition for abstract algebra starting from high school algebra.
In addition to the standard number systems, polynomials, vectors, and matrices,
the first chapter introduces modular arithmetic and dihedral groups. The
second chapter builds on these basic examples and properties, enabling students
to learn structural ideas common to rings and groups: isomorphism, homomorphism
and direct product. The third chapter investigates introductory group
theory. Later chapters delve more deeply into groups, rings, and fields,
including Galois theory, and introduce other topics, such as lattices. The
exposition is clear and conversational throughout.
The book has numerous exercises in each section and
supplemental exercises and projects for each chapter. Many examples and
well over 100 figures provide support for learning. Short biographies introduce
the mathematicians who proved many of the results. The book presents
a pathway to algebraic thinking in a semester- or year-long algebra course.
My geometry textbook, Thinking Geometrically: A Survey of Geometries was published by the MAA/AMS in 2015. The description below is from the back cover.
This survey, unlike most geometry texts, provides both essential geometric
preparation for mathematics education majors and insight and challenge for
mathematics majors. This book’s exercises and text support the development of
both geometric reasoning and intuition. The varied types of exercises and
projects range from elementary exercises to open-ended investigations, enabling
instructors to find suitable exercises to fit their students’ abilities and
challenge them. Topics include those needed for secondary teacher preparation as
well as more wide ranging topics.
My introduction to proofs text, Foundations of Mathematics, was published by Wiley in 2008.
This textbook provides a pedagogically informed introduction to mathematical
proofs, language, and basic structures. The wide variety of exercises enable
students to solidify their understanding, draw connections between topics, and
make conjectures as well as improve their ability to state and prove statements.
There are many incorrect arguments that students are asked to critique.
It uses a conscious pedagogical approach in the first half of introducing
definitions and building intuition for them at least a full section before
expecting students to prove results using them. The second half continues to
build intuition for the formal definitions while expecting students to start
proving results at the same time. The chapter on functions precedes the chapter
on relations to enable students to build on their deeper understanding of
functions to understand the more abstract concept of relations.
The last chapter introduces topics rarely found in undergraduate mathematics
texts: metamathematics, including a discussion of Gödel’s incompleteness
theorems, and the philosophy of mathematics.
Click on North Central Section to go to the section's home page. Click on MAA to go to the home page of the Mathematical Association of America.
You can see a version of my Curriculum vitae by clicking cv.
Mathematics Department Home Page CSB/SJU Home Page
PICTURES
The first picture below shows me judging during the 2000 Donut Coloring Contest. The middle one features some of the students in my 1999 geometry class and their finished tensegrity figure. The picture on the right highlights Math Society students in 1985 making a small stellated rombicosidodecahedron out of straws and string. A more recent stellated rombicosidodecahedron is hanging in the Student Lounge of the Engel Science building at SJU, along with the tensegrity figure.
The views and opinions expressed in this page are strictly those of the author. The contents of this page have not been reviewed or approved by the College of Saint Benedict/Saint John's University.
This web site last updated 27 December, 2023.
